which is a well-established relativistic wave equation for the description of a massive spinless particle. It is manifestly relativistic as for every solution \(\Psi \)  of Eq. (REF ) and every \(g\in \tilde{\mathcal {P}}\)  the transformed wave function \(\Psi _g(\mathfrak {x}):=\Psi (g^{-1}\cdot \mathfrak {x})\)  with \(\mathfrak {x}=(t,x)\)  is still a solution. (For a detailed discussion of Eq. (REF )
see [1]}). We will show explicitly that, in contrast to what holds for the Dirac and Weyl equations, the multiplication of \(\Psi \)  by the space variables \(x_j\) , \(j=1,2,3\)  and by the indicator functions \(1_\Delta \)  of measurable sets \(\Delta \subset \mathbb {R}^3\)  does not define observables as these operators turn out to be not self-adjoint.
This failure is expected due to the fact that otherwise the canonical PM \(E(\Delta )\Psi :=1_\Delta \Psi \)  would (as in the Dirac and Weyl cases) constitute a causal WL, which as we know does not exist.
